Reliability for some bivariate exponential distributions

In the area of stress-strength models, there has been a large amount of work as regards estimation of the reliability R = Pr( X < Y). The algebraic form for R = Pr( X < Y) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, forms of R are considered when ( X, Y) follow bivariate distributions with dependence between X and Y. In particular, explicit expressions for R are derived when the joint distribution is bivariate exponential. The calculations involve the use of special functions. An application of the results is also provided.